Relationship between the standard error of the estimators and the standard error of the error term [closed]

0

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I'm trying to solve the following problem:

---

My thinking is that If the Standard error of the error term would then the error term of the regression would also fall (as the regression would start performing better).

statistics regression standard-deviation linear-regression

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edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

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closed as off-topic by d80d2729a352b1366139fc119d3345, Riccardo.Alestra, Adrian Keister, Lee David Chung Lin, Leucippus Jan 26 at 0:09

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0

$begingroup$

I'm trying to solve the following problem:

---

My thinking is that If the Standard error of the error term would then the error term of the regression would also fall (as the regression would start performing better).

statistics regression standard-deviation linear-regression

share|cite|improve this question

edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

$endgroup$

closed as off-topic by d80d2729a352b1366139fc119d3345, Riccardo.Alestra, Adrian Keister, Lee David Chung Lin, Leucippus Jan 26 at 0:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Lee David Chung Lin, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

add a comment | 

0

0

0

$begingroup$

I'm trying to solve the following problem:

---

My thinking is that If the Standard error of the error term would then the error term of the regression would also fall (as the regression would start performing better).

statistics regression standard-deviation linear-regression

share|cite|improve this question

edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

$endgroup$

I'm trying to solve the following problem:

---

My thinking is that If the Standard error of the error term would then the error term of the regression would also fall (as the regression would start performing better).

statistics regression standard-deviation linear-regression

statistics regression standard-deviation linear-regression

share|cite|improve this question

edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

share|cite|improve this question

edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

share|cite|improve this question

share|cite|improve this question

edited Jan 25 at 9:57

Fozoro

edited Jan 25 at 9:57

Fozoro

edited Jan 25 at 9:57

Fozoro

asked Jan 25 at 9:31

FozoroFozoro

1265

asked Jan 25 at 9:31

FozoroFozoro

1265

asked Jan 25 at 9:31

FozoroFozoro

1265

1265

closed as off-topic by d80d2729a352b1366139fc119d3345, Riccardo.Alestra, Adrian Keister, Lee David Chung Lin, Leucippus Jan 26 at 0:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Lee David Chung Lin, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by d80d2729a352b1366139fc119d3345, Riccardo.Alestra, Adrian Keister, Lee David Chung Lin, Leucippus Jan 26 at 0:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Adrian Keister, Lee David Chung Lin, Leucippus

If this question can be reworded to fit the rules in the help center, please edit the question.

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1 Answer
1

active

oldest

votes

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You are right, e.g., for the slope
$$
Var(hat{beta}_1) =frac{1}{(sum(x_i - bar{x})^2)^2}Varleft( sum (x_i - bar{x})y_i right) = frac{sigma^2}{sum(x_i - bar{x})^2},
$$
where $Var(epsilon_i) = sigma^2$. For the intercept you have
$$
Var(hat{beta}_0) =frac{sigma^2}{n} + frac{sigma^2bar{x}^2}{sum(x_i - bar{x})^2},
$$
thus reducing the variance of $epsilon_i$ will reduce the standard error of the OLS estimators.

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answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

0

$begingroup$

You are right, e.g., for the slope
$$
Var(hat{beta}_1) =frac{1}{(sum(x_i - bar{x})^2)^2}Varleft( sum (x_i - bar{x})y_i right) = frac{sigma^2}{sum(x_i - bar{x})^2},
$$
where $Var(epsilon_i) = sigma^2$. For the intercept you have
$$
Var(hat{beta}_0) =frac{sigma^2}{n} + frac{sigma^2bar{x}^2}{sum(x_i - bar{x})^2},
$$
thus reducing the variance of $epsilon_i$ will reduce the standard error of the OLS estimators.

share|cite|improve this answer

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

$endgroup$

add a comment | 

0

$begingroup$

You are right, e.g., for the slope
$$
Var(hat{beta}_1) =frac{1}{(sum(x_i - bar{x})^2)^2}Varleft( sum (x_i - bar{x})y_i right) = frac{sigma^2}{sum(x_i - bar{x})^2},
$$
where $Var(epsilon_i) = sigma^2$. For the intercept you have
$$
Var(hat{beta}_0) =frac{sigma^2}{n} + frac{sigma^2bar{x}^2}{sum(x_i - bar{x})^2},
$$
thus reducing the variance of $epsilon_i$ will reduce the standard error of the OLS estimators.

share|cite|improve this answer

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

$endgroup$

add a comment | 

0

0

0

$begingroup$

You are right, e.g., for the slope
$$
Var(hat{beta}_1) =frac{1}{(sum(x_i - bar{x})^2)^2}Varleft( sum (x_i - bar{x})y_i right) = frac{sigma^2}{sum(x_i - bar{x})^2},
$$
where $Var(epsilon_i) = sigma^2$. For the intercept you have
$$
Var(hat{beta}_0) =frac{sigma^2}{n} + frac{sigma^2bar{x}^2}{sum(x_i - bar{x})^2},
$$
thus reducing the variance of $epsilon_i$ will reduce the standard error of the OLS estimators.

share|cite|improve this answer

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

$endgroup$

You are right, e.g., for the slope
$$
Var(hat{beta}_1) =frac{1}{(sum(x_i - bar{x})^2)^2}Varleft( sum (x_i - bar{x})y_i right) = frac{sigma^2}{sum(x_i - bar{x})^2},
$$
where $Var(epsilon_i) = sigma^2$. For the intercept you have
$$
Var(hat{beta}_0) =frac{sigma^2}{n} + frac{sigma^2bar{x}^2}{sum(x_i - bar{x})^2},
$$
thus reducing the variance of $epsilon_i$ will reduce the standard error of the OLS estimators.

share|cite|improve this answer

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

share|cite|improve this answer

share|cite|improve this answer

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

answered Jan 25 at 11:09

V. VancakV. Vancak

11.3k3926

11.3k3926

add a comment | 

add a comment | 

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